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class Set {
ghost var Repr: set<object>;
ghost var elems: set<int>;
var root: SetNode;
function Valid_repr(): bool
reads *;
{
this in Repr &&
null !in Repr &&
(root != null ==> root in Repr && root.Repr <= Repr && this !in root.Repr)
}
function Valid_self(): bool
reads *;
{
Valid_repr() &&
(root == null ==> elems == {}) &&
(root != null ==> elems == root.elems)
}
function Valid(): bool
reads *;
{
this.Valid_self() &&
(root != null ==> root.Valid())
}
method Double(p: int, q: int)
modifies this;
ensures fresh(Repr - {this});
ensures Valid();
ensures elems == {p, q};
{
var gensym67 := new SetNode;
gensym67._synth_Set_Double_gensym67(p, q);
this.elems := {p, q};
this.root := gensym67;
// repr stuff
this.Repr := {this} + this.root.Repr;
}
method Empty()
modifies this;
ensures fresh(Repr - {this});
ensures Valid();
ensures elems == {};
{
this.elems := {};
this.root := null;
// repr stuff
this.Repr := {this};
}
method Singleton(t: int)
modifies this;
ensures fresh(Repr - {this});
ensures Valid();
ensures elems == {t};
{
var gensym67 := new SetNode;
gensym67._synth_Set_Singleton_gensym67(t);
this.elems := {t};
this.root := gensym67;
// repr stuff
this.Repr := {this} + this.root.Repr;
}
method Sum(p: int, q: int)
modifies this;
ensures fresh(Repr - {this});
ensures Valid();
ensures elems == {p + q};
{
var gensym69 := new SetNode;
gensym69._synth_Set_Sum_gensym69(p, q);
this.elems := {p + q};
this.root := gensym69;
// repr stuff
this.Repr := {this} + this.root.Repr;
}
}
class SetNode {
ghost var Repr: set<object>;
ghost var elems: set<int>;
var data: int;
var left: SetNode;
var right: SetNode;
function Valid_repr(): bool
reads *;
{
this in Repr &&
null !in Repr &&
(left != null ==> left in Repr && left.Repr <= Repr && this !in left.Repr) &&
(right != null ==> right in Repr && right.Repr <= Repr && this !in right.Repr)
}
function Valid_self(): bool
reads *;
{
Valid_repr() &&
(elems == ({data} + (if left != null then left.elems else {})) + (if right != null then right.elems else {})) &&
(left != null ==> (forall e :: e in left.elems ==> e < data)) &&
(right != null ==> (forall e :: e in right.elems ==> e > data))
}
function Valid(): bool
reads *;
{
this.Valid_self() &&
(left != null ==> left.Valid_self()) &&
(right != null ==> right.Valid_self()) &&
(left != null && left.left != null ==> left.left.Valid_self()) &&
(left != null && left.right != null ==> left.right.Valid_self()) &&
(right != null && right.left != null ==> right.left.Valid_self()) &&
(right != null && right.right != null ==> right.right.Valid_self())
}
method Double(p: int, q: int)
modifies this;
requires p != q;
ensures fresh(Repr - {this});
ensures Valid();
ensures elems == {p, q};
{
if (q > p) {
var gensym77 := new SetNode;
gensym77._synth_SetNode_Double_gensym77(q);
this.data := p;
this.elems := {p, q};
this.left := null;
this.right := gensym77;
// repr stuff
this.Repr := {this} + this.right.Repr;
} else {
var gensym77 := new SetNode;
gensym77._synth_SetNode_Double_gensym77(p);
this.data := q;
this.elems := {p, q};
this.left := null;
this.right := gensym77;
// repr stuff
this.Repr := {this} + this.right.Repr;
}
}
method _synth_SetNode_Double_gensym77(q: int)
modifies this;
ensures fresh(Repr - {this});
ensures Valid();
ensures elems == {q};
{
this.data := q;
this.elems := {q};
this.left := null;
this.right := null;
// repr stuff
this.Repr := {this};
}
method _synth_SetNode_Triple_gensym80(r: int)
modifies this;
ensures fresh(Repr - {this});
ensures Valid();
ensures elems == {r};
{
this.data := r;
this.elems := {r};
this.left := null;
this.right := null;
// repr stuff
this.Repr := {this};
}
method Triple(p: int, q: int, r: int)
modifies this;
requires p != q;
requires q != r;
requires r != p;
ensures fresh(Repr - {this});
ensures Valid();
ensures elems == {p, q, r};
{
if (p < q && r > q) {
var gensym80 := new SetNode;
var gensym81 := new SetNode;
gensym80._synth_SetNode_Triple_gensym80(r);
gensym81._synth_SetNode_Triple_gensym81(p);
this.data := q;
this.elems := {p, q, r};
this.left := gensym81;
this.right := gensym80;
// repr stuff
this.Repr := ({this} + this.left.Repr) + this.right.Repr;
} else {
if (r < p && q > p) {
var gensym80 := new SetNode;
var gensym81 := new SetNode;
gensym80._synth_SetNode_Triple_gensym80(q);
gensym81._synth_SetNode_Triple_gensym81(r);
this.data := p;
this.elems := {p, q, r};
this.left := gensym81;
this.right := gensym80;
// repr stuff
this.Repr := ({this} + this.left.Repr) + this.right.Repr;
} else {
if (p < r && q > r) {
var gensym80 := new SetNode;
var gensym81 := new SetNode;
gensym80._synth_SetNode_Triple_gensym80(q);
gensym81._synth_SetNode_Triple_gensym81(p);
this.data := r;
this.elems := {p, q, r};
this.left := gensym81;
this.right := gensym80;
// repr stuff
this.Repr := ({this} + this.left.Repr) + this.right.Repr;
} else {
if (r < q && p > q) {
var gensym80 := new SetNode;
var gensym81 := new SetNode;
gensym80._synth_SetNode_Triple_gensym80(p);
gensym81._synth_SetNode_Triple_gensym81(r);
this.data := q;
this.elems := {p, q, r};
this.left := gensym81;
this.right := gensym80;
// repr stuff
this.Repr := ({this} + this.left.Repr) + this.right.Repr;
} else {
if (q < r && p > r) {
var gensym80 := new SetNode;
var gensym81 := new SetNode;
gensym80._synth_SetNode_Triple_gensym80(p);
gensym81._synth_SetNode_Triple_gensym81(q);
this.data := r;
this.elems := {p, q, r};
this.left := gensym81;
this.right := gensym80;
// repr stuff
this.Repr := ({this} + this.left.Repr) + this.right.Repr;
} else {
var gensym80 := new SetNode;
var gensym81 := new SetNode;
gensym80._synth_SetNode_Triple_gensym80(r);
gensym81._synth_SetNode_Triple_gensym81(q);
this.data := p;
this.elems := {p, q, r};
this.left := gensym81;
this.right := gensym80;
// repr stuff
this.Repr := ({this} + this.left.Repr) + this.right.Repr;
}
}
}
}
}
}
method _synth_SetNode_Triple_gensym81(p: int)
modifies this;
ensures fresh(Repr - {this});
ensures Valid();
ensures elems == {p};
{
this.data := p;
this.elems := {p};
this.left := null;
this.right := null;
// repr stuff
this.Repr := {this};
}
method Init(t: int)
modifies this;
ensures fresh(Repr - {this});
ensures Valid();
ensures elems == {t};
{
this.data := t;
this.elems := {t};
this.left := null;
this.right := null;
// repr stuff
this.Repr := {this};
}
method _synth_SetNode__synth_Set_Double_gensym67_gensym77(q: int)
modifies this;
ensures fresh(Repr - {this});
ensures Valid();
ensures elems == {q};
{
this.data := q;
this.elems := {q};
this.left := null;
this.right := null;
// repr stuff
this.Repr := {this};
}
method _synth_Set_Double_gensym67(p: int, q: int)
modifies this;
ensures fresh(Repr - {this});
ensures Valid();
ensures elems == {p, q};
{
if (q > p) {
var gensym77 := new SetNode;
gensym77._synth_SetNode__synth_Set_Double_gensym67_gensym77(q);
this.data := p;
this.elems := {p, q};
this.left := null;
this.right := gensym77;
// repr stuff
this.Repr := {this} + this.right.Repr;
} else {
if (p > q) {
var gensym77 := new SetNode;
gensym77._synth_SetNode__synth_Set_Double_gensym67_gensym77(p);
this.data := q;
this.elems := {p, q};
this.left := null;
this.right := gensym77;
// repr stuff
this.Repr := {this} + this.right.Repr;
} else {
this.data := q;
this.elems := {p, q};
this.left := null;
this.right := null;
// repr stuff
this.Repr := {this};
}
}
}
method _synth_Set_Singleton_gensym67(t: int)
modifies this;
ensures fresh(Repr - {this});
ensures Valid();
ensures elems == {t};
{
this.data := t;
this.elems := {t};
this.left := null;
this.right := null;
// repr stuff
this.Repr := {this};
}
method _synth_Set_Sum_gensym69(p: int, q: int)
modifies this;
ensures fresh(Repr - {this});
ensures Valid();
ensures elems == {p + q};
{
this.data := p + q;
this.elems := {p + q};
this.left := null;
this.right := null;
// repr stuff
this.Repr := {this};
}
}
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